Appendix 6

EXAMPLE OF DELAUNAY TRIANGULATION

Delaunay triangulation is a method or partitioning known information at irregularly distributed data points to allow smooth, local interpolation between the points. It uses the method of natural neighbor interpolation, meaning that the value of an arbitrary point is determined by the three closest points and the relative distance from each. A Delaunay triangulation can be found using the empty circle method, which says that the circle passing through three natural neighbor points will contain no other data points. This creates a unique triangulation for each set of data points. The Delaunay triangulation of an arbitrary set of points is shown below.

VORONOI POLYGONS AND CONVEX HULLS

Voronoi Polygons are dual to Delaunay triangulations (if one is known, the other is also defined). (Sambridge, Braun, McQueen). They essentially divide a map by creating a region around each known point such that every location in the region is closer to that point than to any other on the map. The Delaunay triangles connect points with adjacent edges in a Voronoi diagram. The Voronoi diagram for an arbitrary set of data points is shown below (left). The convex hull (right) is the structure enclosed by the outer most faces of the Voronoi Polygons. In this problem the convex hull represents the boundaries of the area contaminated by the spill.